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Mirrors > Home > ILE Home > Th. List > 3gencl | Unicode version |
Description: Implicit substitution for class with embedded variable. (Contributed by NM, 17-May-1996.) |
Ref | Expression |
---|---|
3gencl.1 | |
3gencl.2 | |
3gencl.3 | |
3gencl.4 | |
3gencl.5 | |
3gencl.6 | |
3gencl.7 |
Ref | Expression |
---|---|
3gencl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3gencl.3 | . . . . 5 | |
2 | df-rex 2354 | . . . . 5 | |
3 | 1, 2 | bitri 182 | . . . 4 |
4 | 3gencl.6 | . . . . 5 | |
5 | 4 | imbi2d 228 | . . . 4 |
6 | 3gencl.1 | . . . . . 6 | |
7 | 3gencl.2 | . . . . . 6 | |
8 | 3gencl.4 | . . . . . . 7 | |
9 | 8 | imbi2d 228 | . . . . . 6 |
10 | 3gencl.5 | . . . . . . 7 | |
11 | 10 | imbi2d 228 | . . . . . 6 |
12 | 3gencl.7 | . . . . . . 7 | |
13 | 12 | 3expia 1140 | . . . . . 6 |
14 | 6, 7, 9, 11, 13 | 2gencl 2632 | . . . . 5 |
15 | 14 | com12 30 | . . . 4 |
16 | 3, 5, 15 | gencl 2631 | . . 3 |
17 | 16 | com12 30 | . 2 |
18 | 17 | 3impia 1135 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 w3a 919 wceq 1284 wex 1421 wcel 1433 wrex 2349 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-gen 1378 ax-ie2 1423 ax-17 1459 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-rex 2354 |
This theorem is referenced by: axpre-ltwlin 7049 axpre-lttrn 7050 axpre-ltadd 7052 axpre-mulext 7054 |
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